Question 214369
In ten years, David will be four times as old as Aaron.  Twenty years ago, David was twice as old as Ellen.  If David is seven years older than Ellen,how old is Aaron?


Step 1.  Let x be the age of Aaron and let y be the age of David


Step 2.  Let y+10=4(x+10) In ten years, David will be four times as old as Aaron.


Step 3.  Let y-7 age of Ellen.


Step 4.  y-20=2(y-7-20)  Twenty years ago, David was twice as old as Ellen.


Step 5.  Solve y in Step 4 and then Solve Step 2 to get age of Aaron.


*[invoke explain_simplification "y-20=2(y-7-20)" ]


Step 6.  Now that y is 34 years.  Then


{{{y+10=4(x+10)}}}


{{{34+10=4x+40}}}


{{{44=4x+40}}}


{{{44-40=4x}}}


{{{4=4x}}}


{{{1=x}}}


Step 7.  ANSWER is Aaron is one year old.


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J